In this "Nota II", which is the continuation of a "Nota I" with the same title published on p. 233 of these «Rendiconti», it is shown that the maximal projective subplanes of an open plane are infinitely generated. It is then deduced that, if a collineation of an open plane has period $2^{i}$, then the subplane formed by its fixed elements is infinitely generated.